Find the number of zeroes at the end of the product 2 × 4 × 6 × 8 × 10 … × 180
a) 1
b) 0
c) 21
d) 120
Sol:
2 × 4 × 6 × 8 × 10 … × 180
⇒ 290(1 × 2 × 3 × 4 × 5 × … × 90)
⇒ 290 × 90!In this case, number of 5’s is less than the number of 2’s. So we need to calculate the number of 5’s Total number of 5’s
= 18 + 3 = 21
Total number of pairs of 2 and 5 = 21
∴ The number of zeroes at the end of the product is 21.
